Prime ends in theory of mappings with finite distortion in the plane | Zendy

Denis Kovtonyuk | Zendy; Igor Petkov | Zendy; Vladimir Ryazanov | Zendy

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Prime ends in theory of mappings with finite distortion in the plane

Author(s) -

Denis Kovtonyuk,

Igor Petkov,

Vladimir Ryazanov

Publication year - 2017

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1705349k

Subject(s) - mathematics , prime (order theory) , lipschitz continuity , boundary (topology) , distortion (music) , generalization , pure mathematics , plane (geometry) , extension (predicate logic) , mathematical analysis , discrete mathematics , combinatorics , geometry , amplifier , cmos , electronic engineering , computer science , engineering , programming language

In the present paper, it was studied the boundary behavior of the so-called lower Q-homeomorphisms in the plane that are a natural generalization of the quasiconformal mappings. In particular, it was found a series of effective conditions on the function Q(z) for a homeomorphic extension of the given mappings to the boundary by prime ends. The developed theory is applied to mappings with finite distortion by Iwaniec, also to solutions of the Beltrami equations, as well as to finitely bi--Lipschitz mappings that a far-reaching extension of the known classes of isometric and quasiisometric mappings.

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